The finishing of Cristiano Ronaldo, Karim Benzema and Gonzalo Higuain put the last eight's outsiders Galatasaray firmly in their place, despite bold pre-match talk that they would take the game to the Jose Mourinho's men.
The gulf in class was evident and Portugal's Ronaldo pulled away onto Mesut Ozil's through-ball to net with a cool lob after only nine minutes, to become the tournament's leading scorer with nine goals.
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Benzema slotted the ball inside Fernando Muslera's near post for the second after 29 minutes and substitute Higuain flicked a header into the top corner at a free-kick in the 73rd.
Galatasaray, backed by raucous support, rarely threatened but when they did keeper Diego Lopez was on hand for the hosts as they kept a first clean sheet of the competition.
"Real Madrid played a very good, balanced match," Real coach Mourinho told a news conference.
"The team worked very hard and to score an early goal makes all the difference. It changes the game."
Asked if he felt confident of progressing in Istanbul next Tuesday, Mourinho sounded a note of caution.
"I know the mentality of some their players and of their coach," he said. "They will look to do something historic. They need a miracle but I have enough experience in football to know miracles happen."
Galatasaray coach Fatih Terim had a dig at referee Svein Oddvar Moen saying he had influenced the result by failing to show cards and by waving away two penalty calls, but was honest about his team's shortcomings.
"Many of our players have a lot of experience but it is very hard playing in such a big stadium in front of so many people," he told a news conference.
DIFFERENCE IN QUALITY
"The difference in quality between the teams and the players is noticeable. I'm sure my players wanted to try things to change the game but they couldn't.
"After a 3-0 result we need a miracle."
There was a crackling atmosphere at the Bernabeu thanks to Galatasaray's impressive number of red and orange draped travelling supporters.
Mourinho sprang a surprise from the start, positioning Michael Essien at right-back instead of Alvaro Arbeloa and the move appeared to pay off as the hosts bossed the game.
Benzema headed just over the bar, and in the ninth minute a swift move led to Ozil bisecting the centre-backs with a diagonal ball and Ronaldo raced through to lift his finish over Fernando Muslera.
He celebrated with his standard 'calm down, I am here' gesture after netting in his fourth consecutive Champions League match, equalling his personal best run which he set in April-October 2012.
Essien's cross from right went over two defenders more worried about Ronaldo in the 29th, and the ball fell at Benzena's feet. He slotted the ball low inside the keeper's near post.
